Secular series and renormalization group for amplitude equations

Kirkinis, E. (2008) Secular series and renormalization group for amplitude equations. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 78(3).

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Abstract

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

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7 citations in Web of Science®

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ID Code: 73431
Item Type: Journal Article
Refereed: Yes
Keywords: Amplitude modulation, Asymptotic analysis, Difference equations, Numerical analysis, Statistical mechanics, Amplitude equations, Asymptotic expansions, First integrals, Non-linear oscillators, Renormalization group, Nonlinear equations
DOI: 10.1103/PhysRevE.78.032104
ISSN: 15393755 (ISSN)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 07 Jul 2014 22:42
Last Modified: 09 Jul 2014 06:29

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